A 2-form between two sup-lattices L and R is defined to be a suplattice bimorphism L×R → 2. Such 2-forms are equivalent to Galois connections, and we study them and their relation to quantales, involutive quantales and quantale modules. As examples we describe applications to C*-algebras.

It is observed that the axioms for partial metrics with values in quantales coincide with the axioms for Q-sets (M -valued sets, sets with fuzzy equality, quantale-valued sets) for commutative quantales. Ω-sets correspond to the case of partial ultrametrics.

Various notions of observing and testing processes are placed in a uniform algebraic framework in which observations are taken as constituting a quantale. General completeness criteria are stated, and proved in our applications. 2 67("/89:&",;&<+*91(8=&>)",#"3185&.781(2"#+.,"3&3.?+*&",;&0(.*188&81/",#+*8

In this research article, a new connection between serial fuzzy relations and an extended version of rough sets in algebraic structure quantale is established. The notion consists successor class overlap the element quantale. Thus approximation space based on via overlaps quantales, are introduced. main purpose study to provide basic structures fuzzy-relations. way, acquires certain appealing p...

We investigate those lax extensions of a Set-monad T = (T,m, e) to the category V-Rel of sets and V-valued relations for a quantale V = (V,⊗, k) that are fully determined by maps ξ : TV → V . We pay special attention to those maps ξ that make V a T-algebra and, in fact, (V,⊗, k) a monoid in the category SetT with its cartesian structure. Any such map ξ forms the main ingredient to Hofmann’s not...

A concept of quantum triad and its solution is introduced. It represents a common framework for several situations where we have a quantale with a right module and a left module, provided with a bilinear inner product. Examples include Van den Bossche quantaloids, quantum frames, simple and Galois quantales, operator algebras, or orthomodular lattices.

A 2-form between two sup-lattices L and R is defined to be a suplattice bimorphism L×R → 2. Such 2-forms are equivalent to Galois connections, and we study them and their relation to quantales, involutive quantales and quantale modules. As examples we describe applications to C*-algebras.

Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new s...